sin165-cos165
=(√2)[sin165°×(√2)/2-cos165°×(√2)/2]
=(√2)[sin165°cos45°-cos165°sin45°]
=(√2)[sin(165°-45°)]
=(√2)sin(120°)
=(√2)sin(180°-60°)
=(√2)sin(60°)
=(√2)(√3)/2
=(√6)/2